We consider pregroup grammars with letter promotions of the form p~(m) ⇒q~(n) , p ⇒ 1, 1 ⇒ q. We prove a variant of Lam-bek's normalization theorem for the calculus of pregroups enriched with such promotions and present a polynomial parsing algorithm for the corresponding pregroup grammars. The algorithm extends that from , elaborated for pregroup grammars without letter promotions. The normalization theorem, restricted to letter promotions without 1, was proved in while the present version was stated in without proof and used to show that the word problem for letter promotions with unit is polynomial. Our results are contained in the unpublished PhD thesis .
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